A method and system for frequency oscillation transfer analysis in multi-machine islanding

Abstract

This invention discloses a method and system for frequency oscillation transfer analysis under multi-machine islanding. The method includes: establishing a transfer function; substituting the operating parameters of each operating condition into the transfer function; if stable, determining whether it is stable; if stable, it indicates that the system on the second VSG side is stable; if unstable, jumping to S3.1 to determine the cause of frequency oscillations on the second VSG side and the first VSG side; if unstable, it indicates that the frequency oscillations on the second VSG side are caused by insufficient stability margin of the second VSG side itself. The advantage of this invention is that it more accurately explains the cause of low-frequency oscillations in the system, thereby guiding the design of virtual synchronous machine controller parameters.

Description

Technical Field

[0001] This invention relates to the field of virtual synchronous generator control technology, specifically to a method and system for frequency oscillation transmission analysis under multi-machine islanding. Background Technology

[0002] Grid-based virtual synchronous machines (VSGs), as a crucial technology for the efficient grid integration of renewable energy, have demonstrated significant advantages in improving the grid operating environment and providing active inertia and damping support, which is essential for ensuring the safety and stability of renewable energy grid-connected systems. However, in multi-machine islanding scenarios, the grid cannot provide sufficient inertia support, leading to changes in the coupling effect between the low-power and high-power VSG sides. This causes oscillations or fluctuations in the various output electrical quantities of the VSG system, affecting system stability and potentially even causing system instability. This problem has become a critical issue that urgently needs to be addressed in the current research field of grid-based virtual synchronous machines (VSGs). Therefore, in-depth exploration of the low-frequency oscillation mechanism of the system is of great importance.

[0003] In recent years, various analytical approaches have emerged in the study of the stability of VSG output electrical quantities, covering key issues such as voltage stability, frequency stability, and power oscillation. These methods provide important support for VSG system stability assessment and lay a theoretical foundation for the safe and stable operation of the power grid. For example, Bode plots of the open-loop transfer functions of voltage and frequency can intuitively present the system's stability margin and dynamic characteristics. However, these transfer function-based models still have shortcomings in analyzing voltage and frequency stability after disturbances: on the one hand, the models often lack clear physical orientation, making it difficult to explain why stability or instability occurs; on the other hand, they are not convenient for directly locating the root cause of stability problems.

[0004] In summary, traditional VSG stability analysis is usually based on the stability margin of the open-loop transfer function. However, this method is difficult to analyze the oscillation transmission effect between the low-power VSG side and the high-power VSG side. Therefore, it cannot accurately assess the stability risk of the low-power VSG side and the high-power VSG side, and cannot explain the cause of the low-frequency oscillation of the system. Summary of the Invention

[0005] The technical problem to be solved by this invention is how to more accurately explain the cause of low-frequency oscillations in a system under oscillation transmission conditions, thereby guiding the design of virtual synchronous machine controller parameters.

[0006] This invention solves the above-mentioned technical problems through the following technical means: a frequency oscillation transfer analysis method under multi-machine islanding, applied to a multi-machine islanding system, wherein the multi-machine islanding system consists of a first VSG and a second VSG, the first VSG and the second VSG being connected in parallel at the PCC point (common point), the method comprising:

[0007] S1. Establish the open-loop transfer function of the second VSG side respectively. Open-loop transfer function of the first VSG side Establish the frequency oscillation transfer function transmitted from the second VSG side to the first VSG side. and the frequency oscillation transfer function transmitted from the first VSG side to the second VSG side ; S2. Substitute the operating parameters for each working condition into... and ,like If stable, then judge Is it stable? If stable, it indicates that the second VSG side system is stable; if If unstable, jump to S3.1; if Instability indicates that the frequency oscillation on the second VSG side is caused by insufficient stability margin on the second VSG side itself; similarly, if If stable, then judge Is it stable? If stable, it indicates that the first VSG-side system is stable; if If unstable, jump to S3.2; if Unstable indicates that the frequency oscillation on the first VSG side is caused by insufficient stability margin on the first VSG side itself; S3.1, Using an oscillatory transfer function Determine the cause of frequency fluctuations on the second VSG side; S3.2, Using an oscillatory transfer function Determine the cause of frequency fluctuations on the first VSG side.

[0008] Further, S3.1 includes: Determine the oscillation transfer function If the amplitude at the oscillation frequency point is greater than 0 dB, it indicates that the frequency fluctuation on the second VSG side is caused by the frequency fluctuation on the first VSG side through transmission. If not, it indicates that there is no oscillation transmission effect between the second VSG side and the first VSG side, and the second VSG side is stable.

[0009] Further, S3.2 includes: Determine the oscillation transfer function If the amplitude at the oscillation frequency point is greater than 0 dB, it indicates that the frequency fluctuation on the first VSG side is caused by the frequency fluctuation on the second VSG side through transmission. If not, it indicates that there is no oscillation transmission effect between the first VSG side and the second VSG side, and the first VSG side is stable.

[0010] Furthermore, the second VSG side open-loop transfer function The expression is:

[0011] in, For the Labras operator, , , , Let represent the coupling transfer functions of the second VSG side phase angle and active power, the second VSG side voltage and active power, the second VSG side phase angle and reactive power, and the second VSG side voltage and reactive power, respectively. The damping coefficient of the reactive power loop on the second VSG side. The inertia coefficient of the reactive power loop on the second VSG side. The damping coefficient of the active loop on the second VSG side. The inertia coefficient of the active loop on the second VSG side. Indicates the reference angular frequency.

[0012] Furthermore, the first VSG side open-loop transfer function The expression is:

[0013] in, , , Let represent the coupling transfer functions of the phase angle and active power on the first VSG side, the coupling transfer functions of the phase angle and reactive power on the first VSG side, and the coupling transfer functions of the voltage and reactive power on the first VSG side, respectively. The damping coefficient of the reactive power loop on the first VSG side. The inertia coefficient of the reactive power loop on the first VSG side. The damping coefficient of the active loop on the first VSG side is . The inertia coefficient of the active loop on the first VSG side.

[0014] Furthermore, the frequency oscillation transfer function transmitted from the second VSG side to the first VSG side The expression is:

[0015] in, These represent the active power transfer functions of the output phase angle of the second VSG side to the grid connection point, the active power transfer functions of the output voltage of the second VSG side to the grid connection point, the active power transfer functions of the output phase angle of the first VSG side to the grid connection point, and the active power transfer functions of the voltage of the first VSG side to the grid connection point, respectively.

[0016] Furthermore, the frequency oscillation transfer function transmitted from the first VSG side to the second VSG side The expression is:

[0017] in, This represents the voltage-active power coupling transfer function of the first VSG side.

[0018] This invention also provides a frequency oscillation transfer analysis system under multi-machine islanding, the system comprising: The transfer function construction module is used to establish the open-loop transfer function of the second VSG side. Open-loop transfer function of the first VSG side Establish the frequency oscillation transfer function transmitted from the second VSG side to the first VSG side. and the frequency oscillation transfer function transmitted from the first VSG side to the second VSG side ; The system stability assessment module is used to substitute the operating parameters of each working condition into the system stability assessment module. and ,like If stable, then judge Is it stable? If stable, it indicates that the second VSG side system is stable; if If unstable, jump to the first frequency fluctuation judgment module; if Instability indicates that the frequency oscillation on the second VSG side is caused by insufficient stability margin on the second VSG side itself; similarly, if If stable, then judge Is it stable? If stable, it indicates that the first VSG-side system is stable; if If unstable, proceed to the second frequency fluctuation judgment module; if Unstable indicates that the frequency oscillation on the first VSG side is caused by insufficient stability margin on the first VSG side itself; The first frequency fluctuation judgment module is used to apply the oscillation transfer function. Determine the cause of frequency fluctuations on the second VSG side; The second frequency fluctuation judgment module is used to apply the oscillation transfer function. Determine the cause of frequency fluctuations on the first VSG side.

[0019] Furthermore, the first frequency fluctuation judgment module is also used for: Determine the oscillation transfer function If the amplitude at the oscillation frequency point is greater than 0 dB, it indicates that the frequency fluctuation on the second VSG side is caused by the frequency fluctuation on the first VSG side through transmission. If not, it indicates that there is no oscillation transmission effect between the second VSG side and the first VSG side, and the second VSG side is stable.

[0020] Furthermore, the second frequency fluctuation judgment module is also used for: Determine the oscillation transfer function If the amplitude at the oscillation frequency point is greater than 0 dB, it indicates that the frequency fluctuation on the first VSG side is caused by the frequency fluctuation on the second VSG side through transmission. If not, it indicates that there is no oscillation transmission effect between the first VSG side and the second VSG side, and the first VSG side is stable.

[0021] Furthermore, the second VSG side open-loop transfer function The expression is:

[0022] in, For the Labras operator, , , , Let represent the coupling transfer functions of the second VSG side phase angle and active power, the second VSG side voltage and active power, the second VSG side phase angle and reactive power, and the second VSG side voltage and reactive power, respectively. The damping coefficient of the reactive power loop on the second VSG side. The inertia coefficient of the reactive power loop on the second VSG side. The damping coefficient of the active loop on the second VSG side. The inertia coefficient of the active loop on the second VSG side. Indicates the reference angular frequency.

[0023] Furthermore, the first VSG side open-loop transfer function The expression is:

[0024] in, , , Let represent the coupling transfer functions of the phase angle and active power on the first VSG side, the coupling transfer functions of the phase angle and reactive power on the first VSG side, and the coupling transfer functions of the voltage and reactive power on the first VSG side, respectively. The damping coefficient of the reactive power loop on the first VSG side. The inertia coefficient of the reactive power loop on the first VSG side. The damping coefficient of the active loop on the first VSG side is . The inertia coefficient of the active loop on the first VSG side.

[0025] Furthermore, the frequency oscillation transfer function transmitted from the second VSG side to the first VSG side The expression is:

[0026] in, These represent the active power transfer functions of the output phase angle of the second VSG side to the grid connection point, the active power transfer functions of the output voltage of the second VSG side to the grid connection point, the active power transfer functions of the output phase angle of the first VSG side to the grid connection point, and the active power transfer functions of the voltage of the first VSG side to the grid connection point, respectively.

[0027] Furthermore, the frequency oscillation transfer function transmitted from the first VSG side to the second VSG side The expression is:

[0028] in, This represents the voltage-active power coupling transfer function of the first VSG side.

[0029] The advantages of this invention are: (1) This invention proposes, for the first time, a frequency oscillation propagation analysis method for network-type virtual synchronous machine systems applicable to multi-machine islanding scenarios, from the perspective of frequency oscillation propagation. This method can reveal the coupling relationship and propagation path of frequency oscillations between the second VSG side and the first VSG side of the network-type converter, identify potential oscillation amplification risks at the overall system level, and provide a new technical path for the stability analysis of network-type converters in multi-machine islanding scenarios. It determines whether the system is stable based on each transfer function, and in the case of system instability, determines the cause of frequency fluctuations, guiding the design of virtual synchronous machine controller parameters.

[0030] (2) This invention verifies that the frequency oscillation between the second VSG side and the first VSG side is not necessarily due to insufficient stability margin of each side; it may also be caused by the oscillation transmission effect between the second VSG side and the first VSG side. This effect can induce or aggravate the frequency oscillation of both sides. The intensity of the oscillation transmission effect is quantitatively evaluated based on the amplitude of the oscillation transfer function at the oscillation frequency point. The larger the amplitude, the stronger the oscillation transmission effect between the systems. When the amplitude is greater than 0, it indicates that the risk of oscillation transmission between the systems is high. When the amplitude is less than 0, it indicates that the risk of oscillation transmission between the systems is low. Thus, the overall scheme can more accurately explain the cause of the low-frequency oscillation of the system, thereby guiding the design of the virtual synchronous machine controller parameters.

[0031] (3) To address the limitation of traditional stability criteria based on a single open-loop transfer function in effectively reflecting the oscillation propagation characteristics within a system, this invention proposes a stability analysis method based on hierarchical modeling and power coupling collaborative analysis of the second and first VSG sides. This method derives the open-loop transfer functions of the second and first VSG sides respectively, performs independent stability analysis on both using a frequency domain stability criterion, and then combines this with a power coupling small-signal model to comprehensively assess the overall system stability, thus forming a well-structured and logically clear framework for the stability analysis of a network-type virtual synchronous machine. Furthermore, an oscillation transfer function between the frequencies of the second and first VSG sides is introduced, and the amplitude of this transfer function at the oscillation frequency is used as a quantitative evaluation index to propose a frequency oscillation propagation criterion, which can be used to determine whether frequency oscillations are propagated and the magnitude of the oscillation propagation intensity. This criterion verifies that the generation of system oscillations is not necessarily due to insufficient stability margin of the system itself, but may also be caused by the frequency oscillation propagation effect, thus providing a new theoretical basis for the mechanism analysis and suppression of oscillation problems in multi-machine islanding scenarios. Attached Figure Description

[0032] Figure 1 This is a system topology diagram of a frequency oscillation transfer analysis method for multi-machine islanding disclosed in an embodiment of the present invention; Figure 2 This is a diagram showing the coupling effect of active power, reactive power, output phase angle, and output voltage between the second VSG side and the first VSG side in a frequency oscillation transfer analysis method for multi-machine islanding disclosed in an embodiment of the present invention. Figure 3 This is a schematic diagram of the dual-input dual-output active power closed loop of the second VSG side and the first VSG side in a frequency oscillation transfer analysis method for multi-machine islanding disclosed in an embodiment of the present invention. Figure 4 This is a schematic diagram of single-input single-output active power closed-loop under the coupling effect between the second VSG side and the first VSG side in a frequency oscillation transfer analysis method for multi-machine islanding disclosed in an embodiment of the present invention. Figure 5 This is a flowchart of a frequency oscillation transfer analysis method under multi-machine islanding disclosed in an embodiment of the present invention; Figure 6(a) shows the simulation and Bode plot of operating condition 1 in a frequency oscillation transfer analysis method under multi-machine islanding disclosed in an embodiment of the present invention; Figure 6(b) shows the simulation and Bode plot of operating condition 2 in a frequency oscillation transfer analysis method under multi-machine islanding disclosed in an embodiment of the present invention; Figure 7(a) shows the simulation and Bode plot of operating condition 3 in a frequency oscillation transfer analysis method under multi-machine islanding disclosed in an embodiment of the present invention; Figure 7(b) shows the simulation and Bode plot of operating condition 4 in a frequency oscillation transfer analysis method under multi-machine islanding disclosed in an embodiment of the present invention; Figure 8 This is a schematic diagram of the HIL simulation platform in a frequency oscillation transfer analysis method under multi-machine islanding disclosed in an embodiment of the present invention; Figure 9 The figure shows the experimental results of a frequency oscillation transfer analysis method for multi-machine islanding disclosed in an embodiment of the present invention. Figure 9 (a), (b), (c) and (d) correspond to working conditions 1, 2, 3 and 4, respectively. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0034] Example 1 like Figure 1 As shown, Embodiment 1 of the present invention provides a frequency oscillation transfer analysis method under multi-machine islanding, applied to a multi-machine islanding system. The multi-machine islanding system consists of a first VSG and a second VSG, which are connected in parallel at the PCC point (common point). The second VSG side and the first VSG side both adopt the same virtual synchronous generator (VSG) control structure.

[0035] In the second VSG side control section, the system samples the voltage and current signals of the second VSG side in real time, obtains the instantaneous active and reactive power of the system via the power calculation module, and introduces them as inputs into the power control loop. For example... Figure 1 In the control block diagram shown, the power control loop consists of two parts: an active power loop and a reactive power loop. In the active power loop, the active power deviation is used as the input signal, which passes through the integral regulator and the feedback channel in sequence to realize the dynamic adjustment and correction of the phase angle of the virtual synchronous generator (VSG) and output the phase angle. θ In the reactive power control loop, the reactive power deviation rate is used as the input signal. Through integral regulation and feedback mechanisms, a control quantity is output to adjust the inverter output voltage amplitude. The phase angle command and voltage amplitude command obtained from the active power loop and reactive power loop respectively are further used to generate the target output voltage signal through a space vector synthesis method, and the inverter is driven by sinusoidal pulse width modulation (SPWM). The control strategy on the first VSG side is consistent with that on the second VSG side.

[0036] Figure 1 The second VSG DC side of the main circuit section adopts a capacitor and resistor equivalent DC voltage source. The filter capacitor is used for modeling. Since this invention focuses on the low-frequency range, the filter capacitor has the characteristic of passing low frequencies and blocking high frequencies. Therefore, the influence of the filter capacitor is not considered in the modeling. This refers to the three-phase voltage on the load side. and These represent the d-axis and q-axis components of the load-side voltage, respectively. and These represent the d-axis and q-axis components of the load-side current, respectively. for m Phase angle at the node for For small signal components, the Mean module is the average value calculation module. The PLL is the phase-locked loop module. for m Frequency at the node This represents the average frequency on the first VSG side. and The filter resistor and filter inductor for the second VSG. and The filter resistor and filter inductor for the first VSG. and For the line resistance and line inductance of the second VSG, and The line resistance and line inductance of the first VSG are given.

[0037] The process of establishing the oscillation propagation analysis framework for grid-type converters in multi-machine islanding scenarios is as follows: like Figure 1 The diagram shows the grid hardware circuit topology of a grid-connected converter in a multi-machine islanding scenario. Based on Kirchhoff's laws, the voltage relationships between the second VSG side, the first VSG side, and the load side are derived as follows: (1) (2) (3) In equations (1)-(3), and These represent the d-axis and q-axis components of the output current on the second VSG side, respectively. and These represent the d-axis and q-axis components of the output current on the first VSG side, respectively. For the second VSG side inductor and , For the second VSG side resistance and , For the first VSG side inductor and , For the first VSG side resistor and ; For load resistance; For load inductance; This represents the reference angular frequency (314 rad / s). The phase angle of the first VSG side. The phase angle on the second VSG side. for m Phase angle at the node for m Voltage amplitude at the node. This indicates the output voltage on the second VSG side. This indicates the output voltage on the first VSG side.

[0038] Based on Kirchhoff's laws, the current signal equation of the VSG system is: (4) (5) Applying small-signal equations (1) to (5) yields the voltage and current small-signal equations for the second VSG side and the first VSG side as follows: (6) (7) (8) (9) in, , , , All are first intermediate parameters and , and They represent , Small signal components; and They represent Small signal components; , These represent the d-axis and q-axis components of the output voltage on the second VSG side, respectively. , These represent the d-axis and q-axis components of the output voltage on the first VSG side, respectively. and They represent , small signal components, and They represent , small signal components, express small signal components, express small signal components, express steady-state value, express small signal components, express steady-state value, express steady-state value, express small signal components, express The steady-state value. This is a small semaphore flag; index 0 represents the steady-state value. Other values ​​below... The meaning of the parameter with subscript 0 is the same, so I will not repeat it.

[0039] The active and reactive power on the second VSG side and the first VSG side can be expressed as follows: (10) in, and These represent the actual active power outputs on the second VSG side and the first VSG side, respectively. and These represent the actual reactive power outputs on the second VSG side and the first VSG side, respectively.

[0040] The load-side power equation can be expressed as: (11) in, This represents the actual active power input to the load.

[0041] By performing small-signal modeling on the power equation (10), the small-signal linearized equations for the active and reactive power on the second VSG side and the first VSG side are obtained as follows: (12) Small-signal linearization of the load-side power equation in equation (11) yields: (13) in, For the Labras operator.

[0042] according to Figure 1 From the control structure in the diagram, the rotor motion equations for the second VSG side and the first VSG side can be obtained as follows: (14) (15) In formulas (14) and (15), The damping coefficient of the reactive power loop on the first VSG side. The inertia coefficient of the reactive power loop on the first VSG side. The damping coefficient of the active loop on the first VSG side is . The inertia coefficient of the active loop on the first VSG side; The damping coefficient of the reactive power loop on the second VSG side. The inertia coefficient of the reactive power loop on the second VSG side. The damping coefficient of the active loop on the second VSG side. The inertia coefficient of the active loop on the second VSG side. and These are the active power reference values ​​for the second VSG side and the first VSG side, respectively. and These are the reactive power reference values ​​for the second VSG side and the first VSG side, respectively. This is the reference value for the grid voltage.

[0043] like Figure 2 As shown, considering the coupling effect between active and reactive power, and based on the power conservation at the PCC point (common point), we can obtain... , , The actual reactive power input to the load. for The small signal component. The phase angle and voltage relationship between the first VSG side and the second VSG side can be obtained based on the rotor motion equation, i.e., formulas (14)-(15). Figure 2 middle , , and These represent the active power transfer function from the second VSG side to the phase angle, the active power transfer function from the first VSG side to the phase angle, the reactive power transfer function from the second VSG side to the voltage, and the reactive power transfer function from the first VSG side to the voltage, respectively. , , , .

[0044] Therefore, the coupling relationship between the active power, output phase angle, and output voltage of the second VSG side and the first VSG side is as follows: (16) in, , , , Let represent the coupling transfer functions of the second VSG side phase angle and active power, the second VSG side voltage and active power, the second VSG side phase angle and reactive power, and the second VSG side voltage and reactive power, respectively. , , , These represent the coupling transfer functions of the first VSG side phase angle and active power, the first VSG side voltage and active power, the first VSG side phase angle and reactive power, and the first VSG side voltage and reactive power, respectively. , , , , , , and The expression is as follows:

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052] in, These represent the active power transfer functions of the output phase angle of the second VSG side to the grid connection point, the active power transfer functions of the output voltage of the second VSG side to the grid connection point, the active power transfer functions of the output phase angle of the first VSG side to the grid connection point, and the active power transfer functions of the voltage of the first VSG side to the grid connection point, respectively. The expression is: (17) in 、 、 、 、 、 、 、 、 、 、 、 、 、 、 and All are second intermediate parameters, and the expression is as follows:

[0053]

[0054] according to Figure 1 As shown in the circuit topology diagram, the output active power on the second VSG side and the first VSG side are equal to the active power on the load side. The small-signal equation for power conservation can be expressed as: (18) Combining formulas (16) and (13), we can obtain... (19) According to formulas (17) and (18), the second VSG side can be coupled to the first VSG side, and the control flow diagram is as follows. Figure 2 As shown.

[0055] according to Figure 3 The frequency oscillation transfer function transmitted from the first VSG side to the second VSG side can be derived from the control flowchart. and the frequency oscillation transfer function transmitted from the second VSG side to the first VSG side The formula is: (20) (twenty one) in, This is the output frequency of the second VSG side. This is the output frequency of the first VSG side. Figure 3 middle This indicates that the phase angle of the second VSG side is transferred to the voltage transfer function and , This represents the phase angle transfer function from the first VSG side to the voltage transfer function. .

[0056] according to Figure 4 The open-loop transfer functions for the second VSG side and the first VSG side can be obtained as follows: (twenty two) (twenty three) in and These are the open-loop transfer functions of the second VSG side and the first VSG side, respectively.

[0057] Based on the above process, a complete analytical framework for the frequency oscillation transmission model in a multi-machine island scenario can be established.

[0058] To further clarify the analytical framework, refer to Figure 5 , Figure 5 A flowchart illustrating the analysis framework for a frequency oscillation propagation model in a multi-machine islanded scenario is provided. The specific analysis steps of the framework are as follows: Step 1: Initialize and linearize the system. First, establish small-signal models of the output phase angle and output voltage amplitude for the second VSG side and the first VSG side respectively. Second, establish the open-loop transfer function for the second VSG side respectively. Open-loop transfer function of the first VSG side Establish the frequency oscillation transfer function transmitted from the second VSG side to the first VSG side. and the frequency oscillation transfer function transmitted from the first VSG side to the second VSG side .

[0059] Step 2: Substitute the operating parameters for each working condition into... and To determine the stability of the second VSG side compared to the first VSG side. If If stable, proceed to step 2.1; if... Unstable operation indicates that the frequency oscillation on the second VSG side is caused by insufficient stability margin on the second VSG side itself. Similarly, if If stable, proceed to step 2.2; if... If it is unstable, it indicates that the frequency oscillation on the first VSG side is caused by insufficient stability margin of the first VSG side itself. Stable refers to The stability margin is greater than 0 dB. Stable refers to The stability margin is greater than 0 dB.

[0060] Step 2.1: In Under stable conditions, further judgment Is it stable? If stable, it indicates that the second VSG side system is stable; if If unstable, proceed to step 3.1.

[0061] Step 2.2: In Under stable conditions, further judgment Is it stable? If stable, it indicates that the first VSG-side system is stable; if If unstable, proceed to step 3.2.

[0062] Step 3.1: Determine the oscillation transfer function If the amplitude at the oscillation frequency point is greater than 0 dB, it indicates that the frequency fluctuation on the second VSG side is caused by the frequency fluctuation on the first VSG side through transmission. If not, it indicates that there is no oscillation transmission effect between the second VSG side and the first VSG side, and the second VSG is stable.

[0063] Step 3.2: Determine the oscillation transfer function If the amplitude at the oscillation frequency point is greater than 0 dB, it indicates that the frequency fluctuation on the first VSG side is caused by the frequency fluctuation on the second VSG side through transmission. If not, it indicates that there is no oscillation transmission effect between the first VSG side and the second VSG side, and the first VSG side is stable. Figure 5 middle For the first VSG frequency, This is the second VSG frequency.

[0064] To verify the correctness of the above analysis framework, four sets of operating conditions were set up for comparison and verification. Analysis and explanation were conducted for the second VSG side and the first VSG side under two scenarios: "oscillation transmission occurs" and "oscillation transmission does not occur." The four sets of operating conditions are numbered 1 to 4, and the circuit topology parameters are set differently for each condition. The analysis process for each condition is as follows... Figure 5 The flowchart shown corresponds to each item, thereby verifying the effectiveness and consistency of the analysis framework.

[0065] As shown in Figure 6(a), simulation results in operating condition 1 show that the frequencies of both the second VSG side and the first VSG side exhibit equal-amplitude oscillation characteristics. At this time, the stability margin of the second VSG side is... The 1.2-degree stability margin is consistent with the constant-amplitude oscillation phenomenon; while the stability margin on the first VSG side is 12 degrees, theoretically indicating a stable state. Furthermore, at the oscillation frequency, the oscillation transfer function... The amplitude is greater than 0 dB, indicating an oscillation transmission effect from the second VSG to the first VSG. That is, the oscillation on the second VSG side is transmitted to the first VSG side through the coupling channel, thereby inducing oscillation on the theoretically stable first VSG side. The above analysis conclusions are consistent with the simulation phenomena.

[0066] As shown in Figure 6(b), simulation results in operating condition 2 show that the frequencies of the second VSG side and the first VSG side also exhibit equal-amplitude oscillations. At this time, the stability margin of the second VSG side is... The 1.8-degree amplitude is consistent with the characteristics of constant-amplitude oscillations; while the stability margin on the first VSG side is 16.4 degrees, which, according to theoretical analysis, should indicate a stable state. Furthermore, at the oscillation frequency, the oscillation transfer function... The amplitude is greater than 0 dB, indicating an oscillation transmission effect from the first VSG to the second VSG. That is, the oscillation on the first VSG side is transmitted to the second VSG side through the coupling channel, thereby inducing oscillation on the theoretically stable second VSG side. The above analysis conclusions are consistent with the simulation phenomena.

[0067] As shown in Figure 7(a), simulation results in operating condition 3 show that the frequencies of both the second and first VSG sides oscillate, but the oscillation amplitudes differ, with the second VSG side exhibiting a significantly larger amplitude than the first VSG side. At this point, the stability margin of the second VSG side is 1.8 degrees, while the stability margin of the first VSG side is 7.5 degrees, indicating a weak oscillation state according to theoretical analysis. Furthermore, at the oscillation frequency, the oscillation transfer function... The amplitude is less than 0 dB, indicating that there is no oscillation transmission effect from the second VSG to the first VSG. That is, the oscillation on the second VSG side is not transmitted to the first VSG side through the coupling channel, so the first VSG side maintains its weak oscillation state. The above analysis conclusion is consistent with the simulation phenomenon.

[0068] As shown in Figure 7(b), simulation results in operating condition 4 indicate that the frequencies of both the second and first VSG sides oscillate, with different amplitudes. The amplitude of the oscillation on the first VSG side is significantly greater than that on the second VSG side. At this point, the stability margin on the first VSG side is 1.2 degrees, and the stability margin on the second VSG side is 7.8 degrees, which, according to theoretical analysis, indicates a weak oscillation state. Furthermore, at the oscillation frequency, the oscillation transfer function... The amplitude is less than 0 dB, indicating that there is no oscillation transmission effect from the first VSG to the second VSG. That is, the oscillation on the first VSG side is not transmitted to the second VSG side through the coupling channel, so the second VSG side maintains its weak oscillation state. The above analysis conclusion is consistent with the simulation phenomenon.

[0069] To further verify the correctness of this analytical framework, this invention includes an experimental verification section, where the circuit parameters and control parameters are consistent with the simulation parameters. The experimental verification section is as follows: To further verify the accuracy and robustness of the proposed grid impedance disturbance model, this invention conducts experimental verification on a hardware-in-the-loop (HIL) experimental platform. For example... Figure 8As shown, the experimental system mainly consists of a HIL real-time simulation model, a controller, an I / O board, an oscilloscope, and a host computer (PC) for system configuration and data recording. The HIL real-time simulation model models the power circuit in real time with a simulation step size of 1 μs, thus enabling high-precision capture of the system's dynamic response characteristics. Simultaneously, the controller samples and executes the aforementioned frequency oscillation transfer analysis method under multi-machine islanding at a sampling frequency of 10 kHz, ensuring that the control algorithm can be executed in real-time, stably, and accurately during the HIL experiment, thereby providing reliable experimental support for verifying the effectiveness of the proposed model.

[0070] Figure 9 Experimental results of the proposed method are presented, where (a), (b), (c), and (d) correspond to operating conditions 1, 2, 3, and 4, respectively. The parameter settings used in the experiments were consistent with the simulation parameters to ensure the comparability of the experimental and simulation results. Figure 9 It can be seen that, under different operating conditions, the experimental results and simulation results show good consistency in overall trends and key characteristics, indicating that the established model can accurately reflect the actual operating state of the system. These results fully verify the effectiveness and correctness of the method proposed in this invention.

[0071] In summary, the technical principles and processes of this invention are summarized as follows: Traditional VSG stability analysis typically relies on the stability margin of the open-loop transfer function. However, this method struggles to analyze the oscillation transfer effect between the second and first VSG sides, thus failing to accurately assess the stability risk of both sides. Specifically, even if the system's open-loop transfer function shows sufficient stability margin, the system may still exhibit varying degrees of oscillation and instability. In such cases, relying solely on the traditional open-loop transfer function stability criterion becomes ineffective. Therefore, this invention proposes an oscillation transfer effect analysis method for both the second and first VSG sides to overcome the shortcomings of traditional open-loop stability analysis methods. A schematic diagram of the system topology is shown below. Figure 1 As shown, the second VSG side adopts a grid-type VSG control, and the first VSG side adopts a high-power capacity grid-type VSG control. The generation mechanism of frequency oscillation between the second VSG side and the first VSG side is revealed in depth, and it is verified that the frequency oscillation between the second VSG side and the first VSG side does not necessarily originate from insufficient stability margin of each side; it may also be caused by the oscillation transmission effect between the second VSG side and the first VSG side, which can induce or aggravate the frequency oscillation of both sides.

[0072] Furthermore, the oscillation transfer model constructed in this invention can quantitatively evaluate the intensity of the oscillation transfer effect based on the amplitude of the oscillation transfer function at the oscillation frequency point. A larger amplitude indicates a stronger oscillation transfer effect between systems; when the amplitude is greater than 0, it indicates a higher risk of oscillation transfer between systems; when the amplitude is less than 0, it indicates a lower risk of oscillation transfer between systems. This criterion has good adaptability and universality, and can provide a theoretical basis for the parameter design of virtual synchronous machine controllers.

[0073] Experimental results demonstrate that this method has good applicability and engineering practical value in new energy power generation systems, effectively revealing the oscillation generation and transmission mechanism between the second VSG side and the first VSG side. This invention sets up four different operating conditions to verify: the case where oscillation transmission occurs / does not occur between the second VSG side and the first VSG side, and the bidirectional transmission case where oscillations from the second VSG side to the first VSG side and from the first VSG side to the second VSG side. The results of each example show that the proposed modeling and analysis method has universality, and the proposed method was verified through hardware-in-the-loop (HIL) experiments. It can provide theoretical basis and engineering guidance for the parameter design of grid-type virtual synchronous machine controllers and the improvement of system robustness. This invention is also applicable to the determination of frequency oscillation transmission effects in multi-machine islanding scenarios under any other control technology.

[0074] Example 2 Based on Embodiment 1, Embodiment 2 of the present invention provides a frequency oscillation transfer analysis system under multi-machine islanding, the system comprising: The transfer function construction module is used to establish the open-loop transfer function of the second VSG side. Open-loop transfer function of the first VSG side Establish the frequency oscillation transfer function transmitted from the second VSG side to the first VSG side. and the frequency oscillation transfer function transmitted from the first VSG side to the second VSG side ; The system stability assessment module is used to substitute the operating parameters of each working condition into the system stability assessment module. and ,like If stable, then judge Is it stable? If stable, it indicates that the second VSG side system is stable; if If unstable, jump to the first frequency fluctuation judgment module; if Instability indicates that the frequency oscillation on the second VSG side is caused by insufficient stability margin on the second VSG side itself; similarly, if If stable, then judge Is it stable? If stable, it indicates that the first VSG-side system is stable; if If unstable, proceed to the second frequency fluctuation judgment module; if Unstable indicates that the frequency oscillation on the first VSG side is caused by insufficient stability margin on the first VSG side itself; The first frequency fluctuation judgment module is used to apply the oscillation transfer function. Determine the cause of frequency fluctuations on the second VSG side; The second frequency fluctuation judgment module is used to apply the oscillation transfer function. Determine the cause of frequency fluctuations on the first VSG side.

[0075] Specifically, the first frequency fluctuation judgment module is also used for: Determine the oscillation transfer function If the amplitude at the oscillation frequency point is greater than 0 dB, it indicates that the frequency fluctuation on the second VSG side is caused by the frequency fluctuation on the first VSG side through transmission. If not, it indicates that there is no oscillation transmission effect between the second VSG side and the first VSG side, and the second VSG side is stable.

[0076] Specifically, the second frequency fluctuation judgment module is also used for: Determine the oscillation transfer function If the amplitude at the oscillation frequency point is greater than 0 dB, it indicates that the frequency fluctuation on the first VSG side is caused by the frequency fluctuation on the second VSG side through transmission. If not, it indicates that there is no oscillation transmission effect between the first VSG side and the second VSG side, and the first VSG side is stable.

[0077] Specifically, the second VSG side open-loop transfer function The expression is:

[0078] in, For the Labras operator, , , , Let represent the coupling transfer functions of the second VSG side phase angle and active power, the second VSG side voltage and active power, the second VSG side phase angle and reactive power, and the second VSG side voltage and reactive power, respectively. The damping coefficient of the reactive power loop on the second VSG side. The inertia coefficient of the reactive power loop on the second VSG side. The damping coefficient of the active loop on the second VSG side. The inertia coefficient of the active loop on the second VSG side. Indicates the reference angular frequency.

[0079] More specifically, the open-loop transfer function on the first VSG side The expression is:

[0080] in, , , Let represent the coupling transfer functions of the phase angle and active power on the first VSG side, the coupling transfer functions of the phase angle and reactive power on the first VSG side, and the coupling transfer functions of the voltage and reactive power on the first VSG side, respectively. The damping coefficient of the reactive power loop on the first VSG side. The inertia coefficient of the reactive power loop on the first VSG side. The damping coefficient of the active loop on the first VSG side is . The inertia coefficient of the active loop on the first VSG side.

[0081] More specifically, the frequency oscillation transfer function transmitted from the second VSG side to the first VSG side. The expression is:

[0082] in, These represent the active power transfer functions of the output phase angle of the second VSG side to the grid connection point, the active power transfer functions of the output voltage of the second VSG side to the grid connection point, the active power transfer functions of the output phase angle of the first VSG side to the grid connection point, and the active power transfer functions of the voltage of the first VSG side to the grid connection point, respectively.

[0083] More specifically, the frequency oscillation transfer function transmitted from the first VSG side to the second VSG side The expression is:

[0084] in, This represents the voltage-active power coupling transfer function of the first VSG side.

[0085] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for frequency oscillation transfer analysis under multi-machine islanding, characterized in that, Applied to a multi-machine islanded system, wherein the multi-machine islanded system consists of a first VSG and a second VSG connected in parallel, the method includes: S1. Establish the voltage and current relationships on the first VSG side, the second VSG side, and the load side according to Kirchhoff's laws, and perform small-signal linearization; based on the power conservation relationship at the PCC point, establish a coupling small-signal model between the active power, reactive power, output phase angle, and output voltage of the first VSG side and the second VSG side; then, combining the VSG rotor motion equations of the first and second VSGs, derive the open-loop transfer function of the second VSG side. Open-loop transfer function of the first VSG side Establish the frequency oscillation transfer function transmitted from the second VSG side to the first VSG side. and the frequency oscillation transfer function transmitted from the first VSG side to the second VSG side The second VSG side open-loop transfer function The expression is: in, For the Labras operator, , , , Let represent the coupling transfer functions of the second VSG side phase angle and active power, the second VSG side voltage and active power, the second VSG side phase angle and reactive power, and the second VSG side voltage and reactive power, respectively. The damping coefficient of the reactive power loop on the second VSG side. The inertia coefficient of the reactive power loop on the second VSG side. The damping coefficient of the active loop on the second VSG side. The inertia coefficient of the active loop on the second VSG side. Indicates the reference angular frequency; S2. Substitute the operating parameters for each working condition into... and ,like If stable, then judge Is it stable? If stable, it indicates that the second VSG side system is stable; if If unstable, jump to S3.1; if Instability indicates that the frequency oscillation on the second VSG side is caused by insufficient stability margin on the second VSG side itself; similarly, if If stable, then judge Is it stable? If stable, it indicates that the first VSG-side system is stable; if If unstable, jump to S3.2; if Unstable indicates that the frequency oscillation on the first VSG side is caused by insufficient stability margin on the first VSG side itself; S3.1, Using an oscillatory transfer function Determine the cause of frequency fluctuations on the second VSG side; S3.2, Using an oscillatory transfer function Determine the cause of frequency fluctuations on the first VSG side.

2. The method for frequency oscillation transfer analysis under multi-machine islanding as described in claim 1, characterized in that, S3.1 includes: Determine the oscillation transfer function If the amplitude at the oscillation frequency point is greater than 0 dB, it indicates that the frequency fluctuation on the second VSG side is caused by the frequency fluctuation on the first VSG side through transmission. If not, it indicates that there is no oscillation transmission effect between the second VSG side and the first VSG side, and the second VSG side is stable.

3. The method for frequency oscillation transfer analysis under multi-machine islanding as described in claim 1, characterized in that, S3.2 includes: Determine the oscillation transfer function If the amplitude at the oscillation frequency point is greater than 0 dB, it indicates that the frequency fluctuation on the first VSG side is caused by the frequency fluctuation on the second VSG side through transmission. If not, it indicates that there is no oscillation transmission effect between the first VSG side and the second VSG side, and the first VSG side is stable.

4. The method for frequency oscillation transfer analysis under multi-machine islanding as described in claim 1, characterized in that, The first VSG side open-loop transfer function The expression is: in, , , Let represent the coupling transfer functions of the phase angle and active power on the first VSG side, the coupling transfer functions of the phase angle and reactive power on the first VSG side, and the coupling transfer functions of the voltage and reactive power on the first VSG side, respectively. The damping coefficient of the reactive power loop on the first VSG side. The inertia coefficient of the reactive power loop on the first VSG side. The damping coefficient of the active loop on the first VSG side is . The inertia coefficient of the active loop on the first VSG side.

5. The frequency oscillation transfer analysis method under multi-machine islanding as described in claim 4, characterized in that, Frequency oscillation transfer function transferred from the second VSG side to the first VSG side The expression is: in, These represent the active power transfer functions of the output phase angle of the second VSG side to the grid connection point, the active power transfer functions of the output voltage of the second VSG side to the grid connection point, the active power transfer functions of the output phase angle of the first VSG side to the grid connection point, and the active power transfer functions of the voltage of the first VSG side to the grid connection point, respectively.

6. The method for frequency oscillation transfer analysis under multi-machine islanding as described in claim 5, characterized in that, Frequency oscillation transfer function transferred from the first VSG side to the second VSG side The expression is: in, This represents the voltage-active power coupling transfer function of the first VSG side.

7. A frequency oscillation transfer analysis system under multi-machine islanding, characterized in that, The system includes: The transfer function construction module is used to establish the voltage and current relationships between the first VSG side, the second VSG side, and the load side according to Kirchhoff's laws, and to perform small-signal linearization. Based on the power conservation relationship at the PCC point, a coupled small-signal model is established between the active power, reactive power, output phase angle, and output voltage of the first VSG side and the second VSG side. Then, combined with the VSG rotor motion equations of the first and second VSGs, the open-loop transfer function of the second VSG side is derived. Open-loop transfer function of the first VSG side Establish the frequency oscillation transfer function transmitted from the second VSG side to the first VSG side. and the frequency oscillation transfer function transmitted from the first VSG side to the second VSG side The second VSG side open-loop transfer function The expression is: in, For the Labras operator, , , , Let represent the coupling transfer functions of the second VSG side phase angle and active power, the second VSG side voltage and active power, the second VSG side phase angle and reactive power, and the second VSG side voltage and reactive power, respectively. The damping coefficient of the reactive power loop on the second VSG side. The inertia coefficient of the reactive power loop on the second VSG side. The damping coefficient of the active loop on the second VSG side. The inertia coefficient of the active loop on the second VSG side. Indicates the reference angular frequency; The system stability assessment module is used to substitute the operating parameters of each working condition into the system stability assessment module. and ,like If stable, then judge Is it stable? If stable, it indicates that the second VSG side system is stable; if If unstable, jump to the first frequency fluctuation judgment module; if Instability indicates that the frequency oscillation on the second VSG side is caused by insufficient stability margin on the second VSG side itself; similarly, if If stable, then judge Is it stable? If stable, it indicates that the first VSG-side system is stable; if If unstable, proceed to the second frequency fluctuation judgment module; if Unstable indicates that the frequency oscillation on the first VSG side is caused by insufficient stability margin on the first VSG side itself; The first frequency fluctuation judgment module is used to apply the oscillation transfer function. Determine the cause of frequency fluctuations on the second VSG side; The second frequency fluctuation judgment module is used to apply the oscillation transfer function. Determine the cause of frequency fluctuations on the first VSG side.

8. The frequency oscillation transfer analysis system under multi-machine islanding as described in claim 7, characterized in that, The first frequency fluctuation judgment module is further configured to: Determine the oscillation transfer function If the amplitude at the oscillation frequency point is greater than 0 dB, it indicates that the frequency fluctuation on the second VSG side is caused by the frequency fluctuation on the first VSG side through transmission. If not, it indicates that there is no oscillation transmission effect between the second VSG side and the first VSG side, and the second VSG side is stable.

9. The frequency oscillation transfer analysis system under multi-machine islanding as described in claim 7, characterized in that, The second frequency fluctuation judgment module is also used for: Determine the oscillation transfer function If the amplitude at the oscillation frequency point is greater than 0 dB, it indicates that the frequency fluctuation on the first VSG side is caused by the frequency fluctuation on the second VSG side through transmission. If not, it indicates that there is no oscillation transmission effect between the first VSG side and the second VSG side, and the first VSG side is stable.

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